The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case ... [more ▼]

The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case of noisy measurements is proposed. The efficiency of proposed solution is demonstrated via example of swinging a pendulum with unknown parameters. [less ▲]

New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for ... [more ▼]

New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for consideration of nonperiodic, e.g., chaotic modes. Upper and lower bounds for oscillations amplitude are obtained. The relation between the oscillatority bounds and excitability indices for the systems with the input are established. Control design procedure providing nonlinear systems with oscillatority property is proposed. Examples illustrating proposed results for Van der Pol system, Lorenz system, and Hindmarsh–Rose neuron model as well as computer simulation results are given. [less ▲]

An extension of a backstepping method for the stabilization of nonlinear systems with respect to a set is presented. Robust control laws providing the system with input-to-output stability are proposed ... [more ▼]

An extension of a backstepping method for the stabilization of nonlinear systems with respect to a set is presented. Robust control laws providing the system with input-to-output stability are proposed. Possibilities of non-strict Lyapunov functions’ application are discussed. The differences between a conventional backstepping method and an approach proposed in Kolesnikov (Synergetic Control Theory. Energoatomizdat: Moscow, 1994; 344) are analyzed. Performance of the obtained solutions is demonstrated by computer simulation for pendulum with an actuator example. [less ▲]

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority ... [more ▼]

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority are established and bounds on oscillation amplitude are calculated. [less ▲]